Konstantinos Spiliopoulos



Department of Mathematics and Statistics
Boston University
111 Cummington Street, Boston MA 02215

Office: MCS233D
Tel: +1-617-353-5209
e-mail: kspiliop_at_math.bu.edu
to send me an email replace _at_ by @.


[ Research Interests and Curriculum Vitae | Publications | Distinctions, Awards and Grants | Editorial work | Invited Talks and Conferences | Seminars | Teaching | Links]


Welcome! I am an Associate Professor at the Department of Mathematics and Statistics, Boston University. I am also affiliated with the Center for Information and Systems Engineering, Boston University and I am a junior faculty fellow at the Hariri Institute at Boston University. I completed my PhD at the Department of Mathematics, University of Maryland at College Park, advised by Professor Mark Freidlin and I was at the Division of Applied Mathematics, Brown University as a Prager Assistant Professor from 2009-2012. My undergraduate studies were in Applied Mathematics and Physics at the National Technical University of Athens in Greece. (NTUA).


Research interests:

My research lies broadly in the areas of stochastic processes, statistical learning, applied mathematics and probability, large deviations, multiscale methods, financial mathematics, asymptotic problems for stochastic processes and partial differential equations , statistical inference for stochastic differential equations. In particular: top


Submitted papers:

  1. "Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models", (with Samuel A. Isaacson and Jingwei Ma), 2020, [ArXiv preprint], submitted.
  2. "Asymptotics of Reinforcement Learning with Neural Networks", (with Justin Sirignano), 2019, [ArXiv preprint], submitted.
  3. "Typical dynamics and fluctuation analysis of slow-fast systems driven by fractional Brownian motion", (with Solesne Bourguin and Siragan Gailus), 2019, [ArXiv preprint], submitted.
  4. "Metastability and exit problems for systems of stochastic reaction-diffusion equations", (with Michael Salins), 2019, [ArXiv preprint], submitted.
  5. "Mean field analysis of deep neural networks", (with Justin Sirignano), 2019, [ArXiv preprint], submitted.
  6. "Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum ", (with Justin Sirignano), 2019, [ArXiv preprint], unpublished technical note, available on arxiv.

Book Chapters:

  1. "Importance sampling for metastable and multiscale dynamical systems", Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, (Editors: D. Holcman) , Springer, 2017, pp 29-53, [ArXiv preprint]
  2. "Systemic Risk and Default Clustering for Large Financial Systems", Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015, [SSRN] ,[ArXiv preprint].

Publications:

  1. "Optimal investment and derivative demand under price impact", (with Michail Anthropelos and Scott Robertson), 2020, Mathematical Finance, [ArXiv preprint], to appear.
  2. "Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus", (with Margaret Beck, Eric Cooper and Gabriel Lord), 2020, Journal of Nonlinear Science , [ArXiv preprint], to appear.
  3. "Network effects and default clustering for large systems", (with Jia Yang), 2020, Journal of Applied Mathematical Finance, [ArXiv preprint], to appear.
  4. "Importance sampling for slow-fast diffusions based on moderate deviations", (with Matthew Morse), 2020, SIAM Journal on Multiscale Modeling and Simulation, Vol. 18, No. 1, pp. 315--350. [ArXiv preprint].
  5. "Mean field analysis of neural networks: a law of large numbers", (with Justin Sirignano), 2020, SIAM Journal on Applied Mathematics, Vol. 80, Issue 2, pp. 725--752. [ArXiv preprint].
  6. "Information geometry for approximate Bayesian computation", 2020, SIAM/ASA Journal on Uncertainty Quantification, Vol. 8, Issue 1, pp. 229--260 [ArXiv preprint].
  7. "Optimal scaling of the MALA algorithm with irreversible proposals for Gaussian targets", (with Michela Ottobre and Natesh S. Pillai), 2020, Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 8, pp. 311--361 [ArXiv preprint]
  8. "Stochastic gradient descent in continuous time: a central limit theorem", (with Justin Sirignano), 2019, Stochastic Systems , [ArXiv preprint], to appear.
  9. "Mean field analysis of neural networks: A central limit theorem", (with Justin Sirignano), 2020, Stochastic Processes and their Applications , Volume 130, Issue 3, March 2020, pp. 1820-1852, [ArXiv preprint].
  10. "Pathwise moderate deviations for option pricing", (with Antoine Jacquier), 2019, Mathematical Finance, [ArXiv preprint], to appear.
  11. "Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations", (with Wenqing Hu and Michael Salins), 2019, Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 7, Issue 4, pp. 808-?874, [ArXiv preprint].
  12. "Selection of quasi-stationary states in the Navier-Stokes equation on the torus", (with Margaret Beck and Eric Cooper), 2019, Nonlinearity , Vol. 32, pp. 209--237, [ArXiv preprint].
  13. "Analysis of multiscale integrators for multiple attractors and irreversible Langevin samplers", (with Jianfeng Lu), 2018, SIAM Multiscale Modeling and simulation , Vol. 16, Issue 4, pp. 1859--1883. [ArXiv preprint].
  14. "Discrete-time statistical inference for multiscale diffusions", (with Siragan Gailus), 2018, SIAM Multiscale Modeling and simulation , Vol. 16, Issue 4, pp. 1824--1858, [ArXiv preprint].
  15. "DGM: A deep learning algorithm for solving partial differential equations", (with Justin Sirignano), 2018, Journal of Computational Physics , Vol. 375, pp. 1339--1364, [ArXiv preprint].
  16. "Sequential Monte Carlo for fractional Stochastic Volatility Models", (with Alexandra Chronopoulou), 2018, Quantitative Finance , Vol. 18, Issue 3, pp. 507--517, [ArXiv preprint].
  17. "Indifference pricing for Contingent Claims: Large Deviations Effects", (with Scott Robertson), 2018, Mathematical Finance , Vol. 28, Issue 1, pp. 335--371, [ArXiv preprint].
  18. "Stochastic gradient descent in continuous time", (with Justin Sirignano), 2017, SIAM Journal on Financial Mathematics, Vol. 8, Issue 1, pp. 933--961, [ArXiv preprint]
  19. "Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes", (with Andrew Papanicolaou), 2017, SIAM Journal on Uncertainty Quantification, Vol. 5, pp. 1220-1247, [ArXiv preprint]
  20. "Hypoelliptic multiscale Langevin diffusions: Large deviations, invariant measures and small mass asymptotics", (with Wenqing Hu), 2017, Electronic Journal of Probability, Vol. 22 (2017), paper no. 55, pp. 1-38, [ArXiv preprint]
  21. "Rare event simulation via importance sampling for linear SPDE's", (with Michael Salins), 2017, Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 5, Issue 4, pp. 652-690, [ArXiv preprint].
  22. "The effect of heterogeneity on flocking behavior and systemic risk", (with Fei Fang and Yiwei Sun), 2017, Statistics and Risk Modelling, Vol. 34, No. 3--4, pp. 141-155, [ArXiv preprint]
  23. "Moderate deviations principle for systems of slow-fast diffusions", (with Matthew R. Morse), 2017, Asymptotic Analysis, Vol. 105, No. 3-4, pp. 97-135, [ArXiv preprint].
  24. "The pricing of contingent claims and optimal positions in asymptotically complete markets", (with Michail Anthropelos and Scott Robertson), 2017, Annals of Applied Probability, , Vol. 27, No. 3, pp. 1778-1830, [ArXiv preprint]
  25. "Markov processes with spatial delay: path space characterization, occupation time and properties", (with Michael Salins), 2017, Stochastics and Dynamics , Vol. 17, No. 6, 1750042 (21 pages), [ArXiv preprint].
  26. "Statistical Inference for Perturbed Multiscale Dynamical Systems", (with Siragan Gailus), 2017, Stochastic Processes and their Applications , Volume 127, Issue 2, pp. 419-448, [ArXiv preprint]
  27. "Improving the convergence of reversible samplers", (with Luc Rey-Bellet), 2016, Journal of Statistical Physics , August 2016, Vol. 164, Issue 3, pp. 472-494, [ArXiv preprint].
  28. "Rare event simulation for multiscale diffusions in random environments", 2015, SIAM Multiscale Modeling and Simulation , Vol. 13, No. 4, pp. 1290--1311 [ArXiv preprint].
  29. "Escaping from an Attractor: Importance Sampling and Rest Points I", (with Paul Dupuis and Xiang Zhou), 2015, Annals of Applied Probability , Vol. 25, No. 5, pp. 2909-2958, [ArXiv preprint]
  30. "Irreversible Langevin samplers and variance reduction: a large deviation approach", (with Luc Rey-Bellet), 2015, Nonlinearity , Vol. 28, pp. 2081-2103, [ArXiv preprint]
  31. "Default Clustering in Large Pools: Large Deviations", (with Richard Sowers), 2015, SIAM Journal on Financial Mathematics , Vol. 6, (2015), pp. 86-116, [SSRN], [ArXiv preprint].
  32. "Quenched Large Deviations for Multiscale Diffusion Processes in Random Environments", 2015, Electronic Journal of Probability, Vol. 20, (2015), no. 15, pp. 1-29, [ArXiv preprint]
  33. "Variance reduction for irreversible Langevin samplers and diffusion on graphs", (with Luc Rey-Bellet), 2015, Electronic Communications in Probability, Vol. 20, (2015), no. 15, pp. 1-16, [ArXiv preprint].
  34. "Non-asymptotic performance analysis of importance sampling schemes for small noise diffusions", 2015, Journal of Applied Probability , Vol. 52, pp. 1-14, [ArXiv preprint]
  35. "Large Portfolio Asymptotics for Losses from Default", (with Kay Giesecke, Richard Sowers and Justin A. Sirignano), 2015, Mathematical Finance, Vol. 25, No. 1, (January 2015), pp. 77-114, [SSRN] ,[ArXiv preprint]
  36. "Rare event simulation in the neighborhood of a rest point", (with Paul Dupuis), 2014, Winter Simulation Conference, article in pdf , (IEEE, 2014), pp. 564-573 .
  37. "Filtering the Maximum Likelihood for Multiscale Problems", (with Andrew Papanicolaou), 2014, SIAM Multiscale Modeling and Simulation , Vol. 12, No. 3, pp. 1193-1229, [ArXiv preprint].
  38. "Fluctuations Analysis for Loss from Default", (with Kay Giesecke and Justin A. Sirignano), 2014, Stochastic Processes and their Applications, Volume 124, Issue 7, pp. 2322-2362, [SSRN],[ArXiv preprint].
  39. "Scaling Limits and Exit Law for Multiscale Diffusions", (with Sergio A. Almada), 2014, Asymptotic Analysis, Volume 87, pp. 65-90, [ArXiv preprint].
  40. "Fluctuation analysis and short time asymptotics for multiple scales diffusion processes", 2014, Stochastics and Dynamics, Vol. 14, No.3, pp. 1350026 [ArXiv preprint].
  41. "Maximum likelihood estimation for small noise multiscale disffusions", (with Alexandra Chronopoulou), 2013, Statistical Inference for Stochastic Processes,Volume 16, Issue 3, pp. 237-266, [ArXiv preprint]
  42. "Large Deviations and Importance Sampling for Systems of Slow-Fast Motion", 2013, Applied Mathematics and Optimization, Vol. 67, pp. 123-161, [ArXiv preprint]
  43. "Default Clustering in Large Portfolios: Typical Events", (with Kay Giesecke and Richard Sowers), 2013, Annals of Applied Probability, Volume 23, Number 1, pp. 348-385, [SSRN], [ArXiv preprint].
  44. "Importance Sampling for Multiscale Diffusions", (with Paul Dupuis and Hui Wang), 2012, SIAM Multiscale Modeling and Simulation , Vol. 12, No. 1, pp. 1-27, [ArXiv preprint].
  45. "Large Deviations for Multiscale Diffusions via Weak Convergence Methods", (with Paul Dupuis), 2012, Stochastic Processes and Their Applications, 122, pp. 1947-1987, [ArXiv preprint].
  46. "Large Deviations Principle for a Large Class of One-Dimensional Homogeneous Strong Markov Processes", 2012, Journal of Theoretical Probability, Volume 25, Issue 4, pp. 925-949, [ArXiv preprint]
  47. "Recovery Rates in Investment-Grade Pools of Credit Assets: A Large Deviations Analysis", (with Richard Sowers), 2011, Stochastic Processes and Their Applications, Volume 121, Issue 12, pp. 2861-2898, [SSRN] ,[ArXiv preprint].
  48. "Rare Event Simulation in Rough Energy Landscapes", (with Paul Dupuis and Hui Wang), 2011, Winter Simulation Conference, article in pdf , (IEEE, 2011), pp. 504-515.
  49. "Wiener Process with Reflection in Nonsmooth Narrow Tubes", 2009, Electronic Journal of Probability, Vol. 14, Paper no. 69, pp. 2011-2037 article in pdf
  50. "Method of Moments Estimation of Ornstein-Uhlenbeck Processes Driven by General Levy Process", 2009, Annales de l'I.S.U.P., Volume 53 - Fascicule 2-3, pp. 3-19 [ArXiv preprint]
  51. "Reaction Diffusion Equations with Non-Linear Boundary Conditions in Narrow Domains", (with Mark Freidlin), 2008, Asymptotic Analysis, Volume 59, Number 3-4, pp.227-249 article in pdf
  52. "A note on the Smoluchowski- Kramers approximation for the Langevin equation with reflection", 2007, Stochastics and Dynamics, Vol. 7, No. 2, pp. 141-153 : article in pdf

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Editorial Work:

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Invited Talks and Lectures:

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